We have studied crystallization in poly(ethylene oxide) droplets with volumes ranging over several orders of magnitude. In all samples, homogeneous nucleation is observed, scaling with the volume of the droplet, down to systems with as few as approximately 10 polymer chains. Surprisingly, nucleation is unaffected by the high degree of confinement, despite a large surface-to-volume ratio and the restriction of chains to length scales much smaller than the radius of gyration. Nucleation was also found to be independent of chain length for two molecular weights studied, differing by an order of magnitude. The results suggest that, for these highly supercooled systems, the formation of a nucleus is influenced by its immediate surroundings and does not depend on the entire length of the constituent chains.